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Terms in this set (74)
Population
all members of the group in which we a re interested
sample
subset of data used in a statistical inference
descriptive statistics
study of how data can be summarized effectively to describe the important aspect of large data sets
statistical inference
making forecasts, estimates, or judgements about a larger group from the smaller group actually observed
parameter
any descriptive measure of a population characteristic
sample statistic
descriptive statistics that characterize samples
4 major measurement scales
nominal, ordinal, interval, ratio
nominal scale
weakest level of measurement; categorize data but does not rank them
ordinal scale
3rd strongest; sort data into categories that are ordered with respect to the characteristic along which the scale is used
ex. 1-5 star ranking on mutual funds
interval scale
second strongest; provide ranking and assurance that the differences between scale values are equal. because of this, they can be added or subtracted meaningfully. zero on this scale does not reflect actual zero (absence of something), so we can not use interval scale to form ratios
ex. time, temperature
ratio scales
strongest scale measurement; have all the characteristics of interval scales and a zero point at the origin. can compute ratios and add and subtract amounts within the scale. can apply the widest range of statistical tools to data measured on this scale
ex. rates of return, bond maturity, money
frequency distribution
a tabular display of data summarized into a relatively small number of intervals. work with all types of measurement scales
histogram
a chart of data that have been grouped by a frequency distribution
absolute frequency
describes the number of times a particular value for a variable (data item) has been observed to occur.
relative frequency
the absolute frequency divided by the total number of observations.
cumulative frequency
the relative frequency of all observations occurring before a given
interval
steps to creating a frequency distribution
1) sort data in ascending order
2) calculate the range of the data
3) decide on the number of intervals (k)
4) determine interval width as range/k
5) determine the intervals by successively adding the interval width to the minimum value, stopping after reaching an interval that includes the maximum value
6) count the number of observation in each interval
7) construct a table
measures of central tendecny specify
where the data is centered
cross-sectional data
occur across different observation types at one point in time
time-series data
occur for the same unit of observation across time
arithmetic mean
sum of the observations divided by the number of observations
most commonly used measure of the center of the data
population mean is an example of a
parameter
the sample mean (also called arithmetic average) is an example of a
sample mean statistic
weighted mean
places greater importance on different observations
when we take the weighted average for forward looking data, the weighted mean is called
expected value
Geometric mean
is most frequently used to average rates of change over time or to compute the growth rate of a variable
allows you to compute the average return when there is compounding
if calculating geometric means for values less than 1 ....
1. Add 1.0 to each
2. Calculate the geometric mean
3. Subtract one to arrive at the correct geometric mean
geometric mean is always less than or equal to the
arithmetic mean
difference between arithmetic and geometric mean increase
with greater variability in the data
Harmonic mean
observation's weight is inversely proportional to its magnitude
advantage to harmonic mean
not as influence by outliers as arithmetic
unless all observations have the same value, harmonic mean is
< geometric mean < arithmetic
Returns over time are almost always computed using ....... mean because of
compounding.
geometric
Some indexes (e.g., Value Line) use a geometric mean of returns across securities because it filters out some of the
Volatility: tracks the median
the harmonic mean penalizes for
volatility
When we have an odd number of observations, the median will be the
closest to the middle. (n+1)/2
When we have an even number, the median will be the average of the
two middle values. n/2, (n+2)/2
unimodal
there is a single most frequently occuring value
multimodal
there are more than one most frequently occuring value
Quartiles
quintiles
deciles
percentiles
divide the data into quarters.
divides data into fifths
divides data into tenths
divides data into hundredths
advantage of median
extreme values do not affect it
modal interval
interval with the highest frequency
dispersion
variability around a measure of central tendency
mean return represents return, and dispersion represents
risk
Mean absolute deviation
the arithmetic average of the absolute value of deviations from the mean
variance
the average squared deviation from the mean
if you find the sample variance (not the population variance), what do you need to do to n
subtract it by 1 to account for the fact that the measure of central tendency used, Xbar, is an estimate of the true population parameter and has some uncertainty associated with it.
the standard deviation is
square root of the variance
excel formula for variance (pop and samp)
POP: VAR.P( ), VARP( ),
SAMP: VAR ( ), VAR.S( )
excel formula for stdv pop and samp
POP: STDEV.P( ),
SAMP: STDEV( ), STDEV.S( )
semivariance
average squared deviation below the mean
focuses on the downside risk
semideviation
square root of the semivariance
target semivariance
average squared deviation below some specified target rate, B, and represents the downside risk of being below target B
target semideviation is its positive square root
skewnees
the degree of symmetry in the dispersion of values around the mean
If observations are equally dispersed around the mean, the distribution is said to be
symmetrical
If the distribution has a long tail on one side and a "fatter" distribution on the other side, it is said to be
skewed in the direction of the long tail
Do we need to know chebyshev's inequality? relative dispersion? coefficient of variation? sharp ratio?
...
a distribution with perfect symmetry has skewness of
0
because the equation for skewness cube's the numbers, data sets with large negative/positive values will
skew in the direction of the larger values
positive skewness characteristics
right skewed, left asymmetry, tail extends right, Mode < Median < Mean
negative skewness characteristics
left skewed, right asymmetry, tail extends left, mode > Median > Mean
kurtosis
measures the relative amount of "peakedness" as compared with the normal distribution, which has a kurtosis of 3.
excess kurtosis =
observed kurtosis minus 3
Leptokurtic
(more peaked than the normal; fatter tails, excess kurtosis>0
Platykurtic
(less peaked than the normal; thinner tails, excess kurtosis<0)
Mesokurtic
(equivalent to the normal, excess kurtosis=0)
excel formula for sample skewness and sample excess kurtosis
SKEW( ) AND KURT( )
we use measures of ..... to compare risk and return across differing sets of observations
relative dispersion???????
coefficient of variation (CV)
the ratio of the standard deviation of a set of observations to their mean value, producing a measure of units of risk (stdv) per unit of return (mean).
=stdv/mean
mean excess return =
Rp - Rf
Rp = mean return to the portfolio
Rf = mean return to a risk free asset
sharpe ratio =
(Rp - Rf)/ Sp
Sp = stdv of return on the portfolio
measures the reward, in terms of mean excess return, per unit of risk, as measured by the stdv of return
risk adverse investors prefer ..... sharp ratios
higher
for sharp ratio, the returns on the stock and stdv must be in
annual terms
because yields are quoted in annual terms (needs to be in the same basis)
If returns are monthly, so that the mean return is a monthly return and the standard deviation is
of monthly returns, how do we convert it to an annual basis
Monthly return to annual return: ((1 + return)^12)
-1
◦ Monthly standard deviation to annual standard deviation: s(sqrt of 12)
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